Coexistence of lazy frogs on ℤ

Mark Holmes, Daniel Kious

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Abstract

We study the so-called frog model on with two types of lazy frogs, with parameters respectively, and a finite expected number of dormant frogs per site. We show that for any such and there is positive probability that the two types coexist (i.e. that both types activate infinitely many frogs). This answers a question of Deijfen, Hirscher, and Lopes in dimension one.

Original languageEnglish
Pages (from-to)702-713
Number of pages12
JournalJournal of Applied Probability
Volume59
Issue number3
Early online date28 Jun 2022
DOIs
Publication statusPublished - 28 Sept 2022

Bibliographical note

Funding Information:
The work of Holmes is supported by Future Fellowship FT160100166 from the Australian Research Council.

Keywords

  • Frog model
  • coexistence
  • competing growth
  • random walk

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

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